Finite Group Databasebeta

← #11777079

Subgroups — #11777079

Order 1152.

389 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 389 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊C8C211yesmaximal, characteristic
2#10590297C211yesmaximal, characteristic
3#10590260C211yesmaximal, characteristic
4C3×#4480C211yesmaximal, characteristic, complemented
5C3×#4479C211yesmaximal, characteristic, complemented
6#10589099C211yesmaximal, characteristic, complemented
7#10589097C211yesmaximal, characteristic, complemented
8#68574—31nomaximal
9#68534—31nomaximal
10C2×C8×C3⋊D3—21no—
11C42×C3⋊D3C2211yescharacteristic
12C32×C4⋊C8C2211yescharacteristic
13#63641—21no—
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C3×C4⋊(C3⋊C8)C2211yescharacteristic
16C3×C4⋊(C3⋊C8)C2211yescharacteristic
17C3×C4×C3⋊C8C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63572C411yescharacteristic
20#63572C411yescharacteristic
21#63557—21no—
22#63557C411yescharacteristic
23#63557C411yescharacteristic
24#63555—21no—
25#4835—31no—
26#4835—31no—
27D3×C4⋊C8—31no—
28D3×C4⋊C8—31no—
29D3×C4⋊C8—61no—
30#4685—31no—
31#4685—31no—
32C3×#335—31no—
33C3×#334—31no—
34#4480—31no—
35#4480D311yescharacteristic, complemented
36#4479—31no—
37#4479D311yescharacteristic, complemented
38#4458—31no—
39#4457—31no—
40C2×C4×C3⋊D3C2×C411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3Q811yescharacteristic
43C2×C32×C8—21no—
44C32×C42C2311yescharacteristic
45C4×C3⋊Dic3C2×C411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47C4×C3⋊Dic3Q811yescharacteristic
48C2×C3⋊(C3⋊C8)—21no—
49C8×C3⋊D3—42no—
50C2×C3×C3⋊C8—21no—
51C2×C3×C3⋊C8—21no—
52C2×C3×C3⋊C8C2×C411yescharacteristic
53C2×C3×C3⋊C8C2×C411yescharacteristic
54C2×C3×C3⋊C8C2×C411yescharacteristic
55C2×C3×C3⋊C8C2×C411yescharacteristic
56#1573—91noSylow
57C2×D3×C8—61no—
58C2×D3×C8—61no—
59C2×D3×C8—62no—
60C42×D3—31no—
61C42×D3—31no—
62C42×D3—61no—
63C3×C4⋊C8—21no—
64C3×C4⋊C8—31no—
65C3×C4⋊C8—31no—
66C3×C4⋊C8C2×D311yescharacteristic
67C3×C4⋊C8C2×D311yescharacteristic
68C3×C4×C8—31no—
69C3×C4×C8—31no—
70(C2×D3)⋊C8—31no—
71(C2×D3)⋊C8—31no—
72(C2×D3)⋊C8—31no—
73(C2×D3)⋊C8—31no—
74(C2×D3)⋊C8—61no—
75(C2×D3)⋊C8—61no—
76#815—61no—
77#815—61no—
78Dic3⋊C8—31no—
79Dic3⋊C8—31no—
80Dic3⋊C8—31no—
81Dic3⋊C8—31no—
82Dic3⋊C8—61no—
83Dic3⋊C8—61no—
84Dic3⋊C8—62no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8C2×D311yescharacteristic
91C4×C3⋊C8C2×D311yescharacteristic
92C22×C3⋊D3C4⋊C411yescharacteristic
93C2×C32×C4C22×C411yescharacteristic
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×Q811yescharacteristic
96C2×C3⋊Dic3C4⋊C411yescharacteristic
97C2×C3⋊Dic3C4⋊C411yescharacteristic
98C2×C3⋊Dic3C4⋊C411yescharacteristic
99C4×C3⋊D3—21no—
100C4×C3⋊D3—21no—
101C4×C3⋊D3—21no—
102C4×C3⋊D3—21no—
103C4×C3⋊D3—22no—
104C32×C8—41no—
105C3⋊(C3⋊C8)—41no—
106C3×C3⋊C8—21no—
107C3×C3⋊C8—21no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#432—91no—
113#431—91no—
114C2×C4⋊C8—91no—
115#335—31no—
116#335—91no—
117#334—31no—
118#334—91no—
119C2×C4×D3—31no—
120C2×C4×D3—31no—
121C2×C4×D3—31no—
122C2×C4×D3—31no—
123C2×C4×D3—31no—
124C2×C4×D3—31no—
125C2×C4×D3—61no—
126C2×C4×D3—61no—
127C2×C4×D3—61no—
128C2×C3×C8—22no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—31no—
132C2×C3×C8—31no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C3×C42—21no—
138C3×C42C22×D311yescharacteristic
139C3×C42C22×D311yescharacteristic
140C4×Dic3—31no—
141C4×Dic3—31no—
142C4×Dic3—31no—
143C4×Dic3—31no—
144C4×Dic3—31no—
145C4×Dic3—31no—
146C4×Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—21no—
151C2×C3⋊C8—62no—
152C2×C3⋊C8—61no—
153C2×C3⋊C8—61no—
154C2×C3⋊C8C4×D311yescharacteristic
155C2×C3⋊C8C4×D311yescharacteristic
156C2×C3⋊C8C4×D311yescharacteristic
157C2×C3⋊C8C4×D311yescharacteristic
158D3×C8—124no—
159D3×C8—122no—
160D3×C8—122no—
161C22×C32C2×C4⋊C411yescharacteristic
162C2×C3⋊D3—21no—
163C2×C3⋊D3—21no—
164C2×C3⋊D3#10812yes—
165C32×C4—21no—
166C32×C4#13111yescharacteristic
167C32×C4#13111yescharacteristic
168C32×C4AGL(1,ℤ/8)11yescharacteristic
169C32×C4#13711yescharacteristic
170C3⋊Dic3—21no—
171C3⋊Dic3—21no—
172C3⋊Dic3—21no—
173C22×C8—181no—
174C2×C42—91no—
175C4⋊C8—31no—
176C4⋊C8—31no—
177C4⋊C8—91no—
178C4⋊C8—91no—
179C4⋊C8—91no—
180C4⋊C8—181no—
181C4⋊C8D3211yescharacteristic
182C22⋊C8—91no—
183C22⋊C8—91no—
184C22⋊C8—181no—
185#97—181no—
186C4×C8—31no—
187C4×C8—31no—
188C22×D3—31no—
189C22×D3—31no—
190C22×D3—61no—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—21no—
194C2×C3×C4C2×C4×D311yescharacteristic
195C2×C3×C4C2×C4×D311yescharacteristic
196C2×C3×C4D3×D411yescharacteristic
197C2×C3×C4D3×D411yescharacteristic
198C2×C3×C4D3×Q811yescharacteristic
199C2×C3×C4D3×Q811yescharacteristic
200C2×Dic3—31no—
201C2×Dic3—31no—
202C2×Dic3—31no—
203C2×Dic3—31no—
204C2×Dic3—31no—
205C2×Dic3—31no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C4×D3—62no—
210C4×D3—62no—
211C4×D3—62no—
212C4×D3—62no—
213C4×D3—62no—
214C4×D3—62no—
215C4×D3—61no—
216C4×D3—61no—
217C4×D3—61no—
218C4×D3—61no—
219C4×D3—61no—
220C4×D3—61no—
221C4×D3—61no—
222C4×D3—61no—
223C4×D3—122no—
224C3×C8—42no—
225C3×C8—41no—
226C3×C8—41no—
227C3×C8—61no—
228C3×C8—61no—
229C3×C8—61no—
230C3×C8—61no—
231C3×C8—121no—
232C3×C8—121no—
233C3⋊C8—21no—
234C3⋊C8—21no—
235C3⋊C8—21no—
236C3⋊C8—21no—
237C3⋊C8—41no—
238C3⋊C8—41no—
239C3⋊C8—122no—
240C3⋊C8—121no—
241C3⋊C8—121no—
242C2×C32#42411yescharacteristic
243C2×C32#42811yescharacteristic
244C2×C32C2×#10811yescharacteristic
245C3⋊D3—22no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—91no—
249C2×C8—21no—
250C2×C8—31no—
251C2×C8—31no—
252C2×C8—31no—
253C2×C8—31no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8—181no—
257C2×C8—362no—
258C42—91no—
259C42—91no—
260C42—91no—
261C42C2×D3211yescharacteristic
262C22×C3—21no—
263C22×C3D3×C4⋊C411yescharacteristic
264C22×C3D3×C4⋊C411yescharacteristic
265C2×D3—32no—
266C2×D3—32no—
267C2×D3—62no—
268C2×D3—62no—
269C2×D3—62no—
270C2×D3—61no—
271C2×D3—61no—
272C2×D3—61no—
273C2×D3—61no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4—41no—
281C3×C4#90111yescharacteristic
282C3×C4#90111yescharacteristic
283C3×C4#90711yescharacteristic
284C3×C4#90711yescharacteristic
285C3×C4#91111yescharacteristic
286C3×C4#91411yescharacteristic
287C3×C4#91511yescharacteristic
288C3×C4#91811yescharacteristic
289Dic3—62no—
290Dic3—62no—
291Dic3—61no—
292Dic3—61no—
293Dic3—61no—
294Dic3—61no—
295Dic3—61no—
296Dic3—61no—
297Dic3—121no—
298C32#157311yescharacteristic, complemented, Sylow
299C23—91no—
300C2×C4—91no—
301C2×C4—91no—
302C2×C4—91no—
303C2×C4—182no—
304C2×C4—181no—
305C2×C4—181no—
306C2×C4—181no—
307C2×C4—181no—
308C2×C4#379711yescharacteristic
309C2×C4C4×D3211yescharacteristic
310C2×C4#381111yescharacteristic
311C8—41no—
312C8—61no—
313C8—61no—
314C8—61no—
315C8—61no—
316C8—121no—
317C8—121no—
318C8—361no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3—21no—
322C2×C3#483911yescharacteristic
323C2×C3#483911yescharacteristic
324C2×C3#486111yescharacteristic
325C2×C3#488111yescharacteristic
326C2×C3D3×#10811yescharacteristic
327C2×C3D3×#10811yescharacteristic
328D3—64no—
329D3—62no—
330D3—62no—
331C22—92no—
332C22—181no—
333C22—181no—
334C22#6388311yescharacteristic
335C4—21no—
336C4—181no—
337C4—181no—
338C4—181no—
339C4#6380311yescharacteristic
340C4#6380511yescharacteristic
341C4#6393711yescharacteristic
342C4#6395111yescharacteristic
343C3—21no—
344C3#6853411yescharacteristic, complemented
345C3#6857411yescharacteristic, complemented
346C2—182no—
347C2#1059058311yescharacteristic
348C2#1059070111yescharacteristic
349C2#1059097211yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1573
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C3×#4480C2semidirect
5. C3×#4479C2semidirect
6. #10589099C2semidirect
7. #10589097C2semidirect
35. #4480D3semidirect
37. #4479D3semidirect
298. C32#1573semidirect
344. C3#68534semidirect
345. C3#68574semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3⋊D3×C4⋊C82
#105902972
#105902602
C3×#44802
C3×#44792
#105890992
#105890972
#685743
#685343